Any expression that contains letters, numbers and basic operation signs

+, --, × and ÷ is called an Algebraic Expression.

Examples:

2x, 5y, -20p, 3x + 5y, -9q/8 are a few examples of algebraic expressions.

In the above examples, *x, y, p, q* are the *letters* and 2, 5, -20, -9/8 are the *numbers*, while the *symbols*:
-, +, ÷ are the basic (fundamental) signs of operations.

The Letters are called variables and the numbers before them are called coefficients.

**1. Letters used as symbols for numbers:**

In the algebraic expression 2x, the letter x stands as a symbol for any number. One can choose any number to write for
x . So, x holds a place for any number. One can write
3, 10, 100 or any other number as required for x . Since
x changes or varies based
on what is to be written for it, it is therefore called *Variable*.

What varies is a variable.

Other variables in the above examples for algebraic expression are p, q and y**2. Symbols used to denote Multiplication **

**1. Now consider 2x.**

What does it mean? It means multiplication of 2 and x, i.e., **2 × x**.

**2 × x** is also called product of 2 and x. *Product* refers to multiplication.

In **2x** we know **x** is the variable and we also know it stands as a symbol to write any number for it. In other words, it holds a place to write any number for it.

Then let us see what will 2x become, when numbers like **3, 10, 100 **are written for x

2x means product (multiplication) of 2 and x. So, we get

** 2 × 3 = 6, 2 × 10 =20, 2×100 =200**

**2. Again consider 2x**

It may also be written as 2.x standing for multiplication (product) of 2 and x.

so, we have **2.x = 2.3 = 6 or 2.10 = 20 or 2.100 = 200**, depending on what number is written for x.

In algebraic expressions, dot indicates multiplication

**3. Consider 2x once again.**

It can also be written as 2(x) standing for multiplication of 2 and x

So, we have **2(3) = 6 or 2(10) = 20 or 2(100) =200**, based on what number we choose to write for x

Let us summarize the above three ways of representing multiplication in the table below:

Symbols used to denote Multiplication in Algebraic Expression

2. A parentheses between symbols or numbers

3. Writing no operation sign between symbols (not numbers

Consider examples to understand the three forms of Algebric Expression:

**
1. A dot placed between symbols**

2.x = 2x, x.y = xy, 7.p = 7p and other examples

2. A parentheses between symbols or numbers

2(x) = 2x, x(y) = xy, 7(p) = 7p

3. Writing no operation sign between symbols (not numbers)

2x means 2×y

xy means x×y

7p means 7×p

Important Note:

Number 50 does not stand for product of 5 and 0 i.e., it is not 0, it is just the number 50. Only in Algebraic Expressions symbols like x and y not connected by any operation sign stand for multiplication of x and y.

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3. Symbols used to denote Division

To denote division of x and y, we write x÷y. The algebraic expression x / y also stands for division of x by y

**4. Converting Words into Symbols**

5. Use of Parentheses

**1. To stand for multiplication: **

2(x) means 2 × x, i.e. the product of 2 and x

2(3) = 2 × 3 = 6

x (y) = x × y

**2. To consider an Algebraic Expression as one number**

3(p + q) is one number i.e., the product of 3 and sum of x and y

6. The Substitution Method:

It’s a very important method. It’s the basic method to find values of variables which stand as place holders. Let us see it below:

**Find the value of each of the following algebraic expressions
if x = 2 and y = 3**

1. x + y

*Solution:*

just plug in 2 for x and 3 for y and called this substitution.

x + y = 2 + 3 = 5

**2. 3x + 4y**

*Solution:*

as in 1. above, just plug in 2 for x and 3 for y

3.2 + 4.3 = 6 + 12 = 18

(recall that 3x stands for multiplication of 3 and x and so also 4y)

**3. (2x – 3y)/(3x + 4y)**

*Solution:*

again as in 1 and 2 above, write the given values in x and y